Busy Beaver definition theory
(BB) One of a series of sets of Turing Machine
programs. The BBs in the Nth set are programs of N states that produce a larger finite number of ones on an initially blank tape than any other program of N states. There is no program that, given input N, can deduce the productivity (number of ones output) of the BB of size N.
The productivity of the BB of size 1 is 1. Some work has been done to figure out productivities of bigger Busy Beavers - the 7th is in the thousands.